Session D29: Experimental Techniques: General Velocimetry

2d-LCA - an alternative to x-wires

The 2d-Laser Cantilever Anemometer (2d-LCA) is an innovative sensor for two-dimensional velocity measurements in fluids. It uses a micostructured cantilever made of silicon and SU-8 as a sensing element and is capable of performing mesurements with extremly high temporal resolutions up to 150kHz. The size of the cantilever defines its spatial resolution, which is in the order of 150 $\mu$m only. Another big feature is a large angular range of 180$^{\circ}$ in total. The 2d-LCA has been developed as an alternative measurement method to x-wires with the motivation to create a sensor that can operate in areas where the use of hot-wire anemometry is difficult. These areas include measurements in liquids and in near-wall or particle-laden flows. Unlike hot-wires, the resolution power of the 2d-LCA does not decrease with increasing flow velocity, making it particularly suitable for measurements in high speed flows. Comparative measurements with the 2d-LCA and hot-wires have been carried out in order to assess the performance of the new anemometer. The data of both measurement techniques were analyzed using the same stochastic methods including a spectral analysis as well as an inspection of increment statistics and structure functions. Furthermore, key parameters, such as mean values of both velocity components, angles of attack and the characteristic length scales were determined from both data sets. The analysis reveals a great agreement between both anemometers and thus confirms the new approach.   

Development of a nano-scale crossed hot wire to measure velocity in high Reynolds numbers

In very high Reynolds number flows, accurate velocity measurements with conventional hot wires are often limited due to the size and response of the sensors. The Nano-Scale Thermal Anemometry Probes (NSTAPs), previously developed at Princeton, have been used successfully to acquire well-resolved velocity data in multiple high Re facilities. The NSTAP has displayed superior performance compared to conventional hot wires both in the spatial and temporal resolution. However, until now, NSTAPs have been limited to single component measurements. Here, a novel method to combine two inclined NSTAP probes, forming a nano-scale cross-wire, is presented. This enables simultaneous measurements of two fluctuating velocity components with unprecedented spatial and temporal resolution. The two sensing elements of the new x-NSTAP are about one order of magnitude shorter than the conventional cross-wire and are contained within a volume of about $50\times50\times50\mu$m. The small sensing volume greatly improves the spatial resolution of high Re measurements. The small thermal mass of the new sensors also improves the frequency response to match that of a single component NSTAP. Measurements with the new x-NSTAP are performed in the Superpipe facility at Princeton and results are presented.   

An Evaluation of the Jorqenson Equation

Multi-sensor hot-wire probes require some processing algorithm to obtain components of the velocity vector at the measurement location. The Jorgenson equation (1) is used by numerous investigators for this purpose. There exist various algorithms to extract the velocity components from the recorded voltages. The present contribution is not to evaluate such algorithms; rather, it is to evaluate the agreement between the inferred (from (1)) and the known (measured) velocities for a range of pitch (angle $\alpha$) and yaw (angle $\beta$) orientations of the probe body. That is, the objective is to ``give counsel'' to those investigators who are considering the use of (1). Calibration data from Neal (2010) provide $\vec{V}$ at ($\alpha$, $\beta$) - each $9^{\circ}$ to +/- $36^{\circ}$. Since E($\alpha$, $\beta$) is to represent $\vec{V}$ ($\alpha$, $\beta$), percentage error magnitudes will be presented. \begin{equation} E^2 = A+BV^n_{eff} \;\; \textrm{and} \;\; V^2_{eff} = U^2_{n} + K_{T} U^2_{T} + K_{B} U^2_{B} \end{equation} Jorqenson, F. E. (1971) ``Directional Sensitivity of Wire and Fiber Film Probes, An Experimental Study,'' DISA Information No. 11\\[4pt] Neal, D.R. (2010) ``The Effects of Rotation on the Flow Field Over a Controlled-Diffusion Airfoil'', PhD Michigan State U.   

Four-sensor Hot-Wire Probes: A Calibration and Data Reduction Strategy

Four-sensor hot-wire probes are capable of simultaneously measuring three components of the velocity vector with a high temporal resolution. Effective use of these probes requires sophisticated calibration and data reduction techniques and a number of different approaches have been published. Lavoie and Pollard (2003) evaluated four of these approaches and found them to vary significantly in terms of complexity, computational costs and accuracy of the results. Lavoie and Pollard showed the work of Wittmer (1998) is the least complicated to implement and has the smallest computational expense. The work of Doebbling (1990) has the best accuracy. A new technique for calibration and data reduction will be presented and compared against the methods of Wittmer (1998) and Doebbling (1990), using the same methodology and evaluation criteria. The results will be shown for a double x-array configuration over the calibration region of +/- $36^{\circ}$ in pitch and yaw, but these methods are directly applicable to other four-sensor geometries.\\[4pt] [1] Lavoie, P., Pollard, A. (2003). ``Uncertainty analysis of four-sensor hot-wires and their data-reduction schemes used in the near field of a turbulent jet.'' \textit{Exp Fluids}, 34(3), 358-370.   

An Electromagnetic Gauge Technique for Measuring Shocked Particle Velocity in Electrically Conductive Samples

Electromagnetic velocity (EMV) gauges are a class of film gauges which permit the direct in-situ measurement of shocked material flow velocity. The active sensing element, typically a metallic foil, requires exposure to a known external magnetic field in order to produce motional electromotive force (emf). Due to signal distortion caused by mutual inductance between sample and EMV gauge, this technique is typically limited to shock waves in non-conductive materials. In conductive samples, motional emf generated in the EMV gauge has to be extracted from the measured signal which results from the combined effects of both motional emf and voltage changes from induced currents. An electromagnetic technique is presented which analytically models the dynamics of induced current between a copper disk moving as a rigid body with constant 1D translational velocity toward an EMV gauge, where both disk and gauge are exposed to a uniform external static magnetic field. The disk is modelled as a magnetic dipole loop where its Foucault current is evaluated from the characteristics of the fields, whereas the EMV gauge is modelled as a circuit loop immersed in the field of the magnetic dipole loop, the intensity of which is calculated as a function of space and, implicitly, time. Equations of mutual induction are derived and the current induced in the EMV gauge loop is solved, allowing discrimination of the motional emf. Numerical analysis is provided for the step response of the induced EMV gauge current with respect to the Foucault current in the moving copper sample.   

Statistical correction on LIFPA measurement

Laser Induced Fluorescence Photobleaching Anemometer (LIFPA) has been applied for velocity fluctuation measurement in micro electrokinetic turbulence in microfluidics. However, due to the intrinsic drawback of LIFPA, i.e. single-point and 1D measurement, LIFPA cannot distinguish velocity components on each directions and should rely on Taylor's Hypothesis to get spatial series of velocity. Hence, the measurement will have error compared to the actual flow field. Here, the statistical errors of LIFPA measurement, due to 3D flows and Taylor's Hypothesis, are theoretically estimated. We derived the correction formulas based on the work of Ewing and George (2000) and estimated the correction factor of LIFPA in the direction parallel to laser beam. The influences of directional correction factors on both LIFPA and single-wire Hot-Wire Anemometer (HWA) measurements are also investigated and compared. Later, first derivation variance (FDV) of velocity fluctuation by both Taylor's Hypothesis and Local Taylor's Hypothesis (Pinton and Labbe 1994) are compared in microfluidics. It is found the error due to Taylor's Hypothesis is negligible. And the 3D flow influence on the FDV of velocity fluctuations in LIFPA is smaller than in HWA measurement.   

Application of Lorentz force techniques for flow rate measurement

We report on the progress of the Lorentz force velocimetry (LFV): a contactless non-invasive flow velocity measurement technique. This method has been developed and demonstrated for various applications in our institute and in industry. At applications for weakly conducting fluids such as electrolytes with conductivities in the range of 1 -- 10 S/m the challenging bottleneck is the detection of the tiny Lorentz forces in the noisy environment of the test channel. For the force measurement a state-of-the-art electromagnetic force compensation balance is used. Due to this device the mass of the Lorentz force generating magnets is limited. For enabling larger magnet systems and for higher force signals we have developed and tested a buoyancy based weight force compensation method which will be presented here. Additionally, results of LFV measurements at non-symmetric fluid profiles will be shown. By that an evaluation of the feasibility of this measurement principle for disturbed fluid profiles that are relevant for developing the LFV for weakly conducting fluids towards industrial applications can be made. Additionally a prospective setup for using the LFV for molten salt flows will be explained.   

Deconvolution as a means of correcting turbulence power spectra measured by LDA

Measurement of turbulence power spectra by means of laser Doppler anemometry (LDA) has proven to be a difficult task. Among the problems affecting the shape of the spectrum are noise in the signal and changes in the sample rate caused by unintentional effects in the measuring apparatus or even in the mathematical algorithms used to evaluate the spectrum. We analyze the effect of various causes of bias in the sample rate and show that the effect is a convolution of the true spectrum with various spectral functions. We show that these spectral functions can be measured with the available data from a standard LDA processor and we use this knowledge to correct the measured spectrum by deconvolution. We present results supported by realistic computer generated data using two different spectral estimators, the so-called slotted autocovariance method and the so-called direct method.   

Dead time effects in turbulence spectra measured by burst-mode LDA

Dead time effects in laser Doppler measurements have not so far been considered a major problem. We show how dead time occurs in burst-mode laser Doppler anemometry (LDA) when using a so-called burst-mode LDA processor and describe their effects on the measured power spectra. We show how dead time effects may be caused by more than one seed particle being present in the measurement volume at the same time and explain analytically how dead time causes a reduction in the power in the spectrum at low frequencies and an oscillation in the spectrum at the high frequency end. We also present a realistic model for the data sampled from a processor with dead time and use this model to generate turbulence velocity data in a computer. Finally we compare the spectrum computed from realistic values of dead time and sample rate in the computer generated data and compare this spectrum to a measured spectrum in a free turbulent jet with similar parameters. The excellent agreement between the features of these spectra show that our model and explanation of the dead time effect is a valid one.   

Boundary Wall Shear Measurement with an Automated LDV-Based System

Wall shear stress is one of the most important measurements in boundary layer flows. Getting wall shear measurements is generally quite difficult due to the need to measure very close to the wall, where poor optical access, particle seeding, and wall effects can bias the results. To simplify that process, a novel system was developed by Measurement Science Enterprise (MSE). The microPro consists of a 12 mm diameter miniLDV attached to a micro-translation stage assembled inside a sealed housing. The microPro automatically locates the wall and measures the mean flow speed profile from a point as close as 50 microns from the window. Accurate estimate of the mean wall shear is obtained from the calculation of the wall velocity gradient obtained from the velocity profile data. We measured wall shear stress on a boundary layer plate mounted in a water tunnel across a range of Reynolds numbers and compared the results against skin friction coefficient models. We also introduced bubbles into the boundary layer to measure the change in wall shear stress with changing void fraction. The measurements show good agreement with established data. This work is supported by the Office of Naval Research (grant ONR- N00014-11-1-0031) and MSE.